Question

A gas station sells three types of gas: Regular for $3.00 a gallon, Performance Plus for $3.10 a gallon, and Premium for $3.20 a gallon. On a particular day 5200 gallons of gas were sold for a total of $15,970. Two times as many gallons of Regular as Premium gas were sold. How many gallons of each type of gas were sold that day?

Answer 1

1152 gallons of Performance Plus gas, 1016 gallons of Premium gas, and 2032 gallons of Regular gas were sold that day.

Step-by-step explanation:

Let's denote the number of gallons of Performance Plus gas as x and the number of gallons of Premium gas as y.

According to the problem, two times as many gallons of Regular gas as Premium gas were sold, so the number of gallons of Regular gas would be 2y.

The total number of gallons sold can be expressed as x + 2y + y = 5200, and the total cost can be expressed as:

$3.10x + $3.20y + $3.00(2y)

= $15,970.

Simplifying the equations, we get:

• x + 3y = 5200
• 2x + 5y = 5320

Multiplying the first equation by 2 gives us 2x + 6y = 10400. Subtracting this from the second equation gives us:

2x - 6y = 5320 - 10400

= -5080.

Adding the two equations, we get 0 = -5080 + 5y, which simplifies to 5y = 5080.

Dividing both sides by 5, we get y = 1016.

Substituting this value back into the first equation, we get x + 3(1016) = 5200.

Solving for x, we get x = 1152.

Therefore, 1152 gallons of Performance Plus gas, 1016 gallons of Premium gas, and 2032 gallons of Regular gas were sold that day.